Document Zbl 0851.57037 - zbMATH Open
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\(e\)-invariants and finite covers. II. (English) Zbl 0851.57037
[For Part I see Indiana Univ. Math. J. 24, 659-675 (1975; Zbl 0335.55010)]. For a finite degree \(d\) covering \(\widetilde {M} \to M\) with \(M\) a closed framed manifold, it is known that \(\widetilde{M}\) need not be cobordant to \(dM\) in the framed cobordism ring. For \(d\) an odd prime \(p\), two invariants measuring the difference are the \(e\)-invariant and an invariant \(I_\Delta\). The evaluation of these invariants leads to sums of \(p\)-th roots of unity. This paper uses the invariant theory of the cyclic group \(Z/pZ\) to evaluate the resulting sums.
MSC:
| 57R90 | Other types of cobordism |